The Quandary of Quandles: a Borel Complete Knot Invariant

We show that the isomorphism problems for left distributive algebras, racks, quandles and kei are as complex as possible in the sense of Borel reducibility. These algebraic structures are important for their connections with the theory of knots, links and braids. In particular, Joyce showed that a quandle can be associated with any knot, and this serves as a complete invariant for tame knots. However, such a classification of tame knots heuristically seemed to be unsatisfactory, due to the apparent difficulty of the quandle isomorphism problem. Our result confirms this view, showing that, from a set-theoretic perspective, classifying tame knots by quandles replaces one problem with (a special case of) a much harder problem

Complexity of a knot invariant

The algebraic structures called quandles constitute a complete invariant for tame knots. However, determining when two quandles are isomorphic is an empirically hard problem, so there is some dissatisfaction with quandles as knot invariants. We have confirmed this apparent difficulty, showing within the framework of Borel reducibility that the general isomorphism problem for quandles is as complex as possible

Impact of America\u27s Choice on Student Performance in Duval County, Florida

This study, conducted by the Consortium for Policy Research in Education (CPRE), reports on the impact of the America\u27s Choice school design on student standardized test performance in Duval County, Florida. We present the results of the first two years of the impact of America\u27s Choice in Duval County in elementary and middle schools in writing, reading, and mathematics using test data from 1999-2001. To detect the effects of America\u27s Choice on student learning, we compared the gains in performance of students in America\u27s Choice schools to those of students in other schools in the district. We employed two statistical techniques in order to make the comparisons as fair as possible. First, we controlled for a variety of student and school demographic characteristics, including prior student achievement, in order to isolate the influences of America\u27s Choice on student learning during a one-to-two year period. Second, we used a statistical method called multi-level modeling that allowed us to appropriately model the fact that students are nested within schools and to take into account the fact that we were looking for the effect of a school-level reform effort using individual-level student data

The Impact of America\u27s Choice on Student Performance in Duval County, Florida

The America\u27s Choice School Design is a K-12 comprehensive school reform model designed by the National Center on Education and the Economy. America\u27s Choice focuses on raising academic achievement by providing a rigorous standards-based curriculum and safety net for all students. The goal of America\u27s Choice is to make sure that all but the most severely handicapped students reach an internationally benchmarked standard of achievement in English/language arts and mathematics by the time that they graduate

Indestructibility of Vopenka's Principle

We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to prove the relative consistency of these large cardinal axioms with a variety of statements known to be independent of ZFC, such as the generalised continuum hypothesis, the existence of a definable well-order of the universe, and the existence of morasses at many cardinals.Comment: 15 pages, submitted to Israel Journal of Mathematic

Characterization of BreR Interaction with the Bile Response Promoters breAB and breR in Vibrio cholerae

The Vibrio cholerae BreR protein is a transcriptional repressor of the breAB efflux system operon, which encodes proteins involved in bile resistance. In a previous study (F. A. Cerda-Maira, C. S. Ringelberg, and R. K. Taylor, J. Bacteriol. 190:7441-7452, 2008), we used gel mobility shift assays to determine that BreR binds at two independent binding sites at the breAB promoter and a single site at its own promoter. Here it is shown, by DNase I footprinting and site-directed mutagenesis, that BreR is able to bind at a distal and a proximal site in the breAB promoter. However, only one of these sites, the proximal 29-bp site, is necessary for BreR-mediated transcriptional repression of breAB expression. In addition, it was determined that BreR represses its own expression by recognizing a 28-bp site at the breR promoter. These sites comprise regions of dyad symmetry within which residues critical for BreR function could be identified. The BreR consensus sequence AANGTANAC-N(6)-GTNTACNTT overlaps the -35 region at both promoters, implying that the repression of gene expression is achieved by interfering with RNA polymerase binding at these promoters

The prevalence of sarcopenia in fallers and those at risk of falls in a secondary care falls unit as measured by bioimpedance analysis

Objectives: Sarcopenia is characterised by loss of skeletal muscle mass and strength with adverse outcomes: physical disability, poor quality of life and death. Low muscle mass and strength are risk factors for falls, although there are few data available on the prevalence of sarcopenia in fallers. This study aimed to determine prevalence of sarcopenia in older people referred to a falls clinic. / Methods: Consecutive patients referred to a secondary care falls unit were recruited. Sarcopenia was diagnosed using the European Working Group on Sarcopenia definition (low muscle mass and function) and cut-off points. Bio-impedance measured appendicular skeletal muscle mass. Gait speed and grip strength were functional measures. / Results: Fifty-eight patients were recruited. Mean (SD) grip strength for women and men respectively were 17.9 (4.9) and 29.9(8.7) kg, mean (SD) gait speeds were 0.61(0.18) and 0.72 (0.4) m/s, mean (SD) appendicular skeletal muscle index in women and men were 6.98(1.0) and 7.85 (1.0) kg/m2 (p=0.018). Prevalence of sarcopenia was 9.8% (95% CI=1.6%-18%). / Conclusions: Sarcopenia, as measured by bio-impedance is not uncommon in older people accessing a secondary care falls clinic. Bio-impedance was simple to perform, although further validation against gold standard methods is needed. As nutritional and exercise interventions for sarcopenia are available, simple methods for diagnosing sarcopenia in fallers should be considered

The neonicotinoid imidacloprid, and the pyrethroid deltamethrin, are antagonists of the insect Rdl GABA receptor

A mutation in the second transmembrane domain of the GABA receptor subunit, Rdl, is associated with resistance to insecticides such as dieldrin and fipronil. Molecular cloning of Rdl cDNA from a strain of the malaria mosquito, Anopheles gambiae, which is highly resistant to dieldrin revealed this mutation (A296G) as well as another mutation in the third transmembrane domain (T345M). Wild-type, A296G, T345M and A296G + T345M homomultimeric Rdl were expressed in Xenopus laevis oocytes and their sensitivities to fipronil, deltamethrin, 1,1,1-trichloro-2,2-bis(p-chlorophenyl) ethane (DDT), imidacloprid and spinosad were measured using two-electrode voltage-clamp electrophysiology. Spinosad and DDT had no agonist or antagonist actions on Rdl. However, fipronil, deltamethrin and imidacloprid decreased GABA-evoked currents. These antagonistic actions were either reduced or abolished with the A296G and the A296G + T345M mutations while T345M alone appeared to have no significant effect. In conclusion, this study identifies another mutation in the mosquito Rdl that is associated with insecticide resistance. While T345M itself does not affect insecticide sensitivity, it may serve to offset the structural impact of A296G. The present study also highlights Rdl as a potential secondary target for neonicotinoids and pyrethroids